Devices and methods for selecting intraocular lenses

ABSTRACT

The invention relates to devices and methods for selecting IOLs for implantation and eye models useful with the methods. One method comprises the steps of determining the axial eye length, the pupil size at a desired light level; the desired postoperative refraction; determining an aspheric representation of the corneal curvature and determining the location of the plane of fixation of the IOL following implantation.

This application claim priority to and is a continuation application ofU.S. application Ser. No. 11/270,991, filed on Nov. 11, 2005, now U.S.Pat. No. 8,087,782, which claims priority to provisional application No.60/627,430, filed on Nov. 12, 2004 and foreign application No. SE0402769-4, filed on Nov. 12, 2004, each of which is hereby incorporatedby reference in their entirety.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates generally to devices and methods forselecting an intraocular lens and more specifically to devices andmethods of finding suitable powers and/or locations of intraocularlenses to be implanted into an eye in order to obtain a predeterminedrefractive outcome, taking into account such parameters as theasphericity of the cornea and/or the intraocular lens.

2. Description of the Related Art

U.S. Pat. No. 5,968,095, herein incorporated by reference, refers to amethod of preoperatively selecting the power of an intraocular lens(IOL) to be implanted into an eye having a lens haptic plane. The methodinvolves selecting eye parameters to construct an eye model for findinga correct representation of the intraocular lens as axially positionedin the eye following surgical implantation. However, this method is notdesigned to be applicable when any of the optical surfaces is aspheric.In particular this method is not applicable when using aspheric lensesdesigned to reduce or eliminate the spherical aberration of the cornea.Other commonly applied methods to determine IOL power, such as thewidely used SRK/T formula, and other widely applied methods such as theHoffer Q and Holladay 1 and Holladay 2 formulas, suffer the sameshortcoming in being based on thin lens vergence calculations and/orspherical lens surfaces. Paul-Rolf Preussner et al. disclose analternative method of predicting outcome of choice of IOL model andpower in J Cataract Refract Surg, 2004, Vol. 30, pp. 2077-2083, which isherein incorporated by reference.

As aspheric IOLs capable of correcting spherical aberrations now arebecoming available on the market (e.g., Tecnis® brand of IOL, availablefrom AMO Inc., Santa Ana, Calif.), there is a demand to obtain reliablemethods to select aspheric IOL powers in order to achieve the desiredpatient outcome in terms of spectacle correction and/or image quality.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the present invention may be better understood from thefollowing detailed description when read in conjunction with theaccompanying drawings. Such embodiments, which are for illustrativepurposes only, depict the novel and non-obvious aspects of theinvention. The drawings include the following figures, with likenumerals indicating like parts:

FIG. 1 is a graphical representation of elements of an eye model used invarious embodiments of the present invention.

FIGS. 2 a and 2 b are magnified views of the corneal region of thegraphical representation shown in FIG. 1

FIG. 3 is a flow chart showing a method of selecting an IOL according toone embodiment of the invention.

FIG. 4 is a flow chart showing a method of selecting an IOL according toanother embodiment of the invention.

FIG. 5 is a graphical representation of the elements of computing systemfor selecting an IOL according to embodiments of the present invention.

FIG. 6 is printout of the formulas programmed into each cell of an Excelspreadsheet used to provide the ray tracing program in accordance withembodiments of the present invention.

FIG. 7 is illustrates the numerical result of the calculation in eachcell of an Excel spreadsheet used to provide the ray tracing program inaccordance with embodiments of the present invention.

FIG. 8 is a ray trace of the numerical results presented in FIG. 7.

FIG. 9A-9D are through-focus MTF plots used to determine maximum MTF ofan IOL.

DETAILED DESCRIPTION OF THE DRAWINGS

The present invention is directed to reliable methods and devices forselecting spherical and aspheric intraocular lenses (IOLs) that providea predetermined refractive outcome for patients in need of cataract orrefractive surgery. Embodiments of the invention may be understood byreference FIG. 1, which is a graphical representation of a model of aneye 20 comprising a cornea 22, an iris 24, a retina 26, and an opticalaxis 28. An IOL 30 is disposed within the eye 20, the IOL 30 comprisingan optic 32 and one or more haptics 34 having distal ends 38. Ingeneral, the eye model may consist of the dimensional parametersillustrated by the geometry shown in FIG. 1, for example, the axiallength of the eye (AL) and the anterior chamber depth (ACD). Otherdimensional parameters that may be included in the eye model that arenot shown in FIG. 1 include, but are not limited to, the corneal radius(CR), the corneal power (K), and crystalline lens thickness (LT). Theeye model may also include various other parameters such as, forexample, the refractive indices of the various portions of the eye 20and/or the IOL 30. In certain embodiments, the distal ends 38 of thehaptics 34 are disposed within a plane defined a lens haptic plane(LHP). In other embodiments, other information of the IOL 30 may beincluded in the eye model such as, for example, an effective principalplane of the optic 32 or other information regarding the optic 32 usefulin determining the performance optic 32 and/or the location of the optic32 within the eye 20.

The graphical representation of the eye model illustrated in FIG. 1 alsohas a coordinate system containing a horizontal axis 40 and a verticalaxis 42, which are labeled in units of millimeters. The graphicalrepresentation illustrated in FIG. 1 also shows a plurality of rays 44entering cornea 22 and the IOL 30 of the eye model. The plurality ofrays 44 comprises a paraxial ray 50 that is disposed near the opticalaxis 28 and a marginal ray 52 that is disposed near edge of the openingformed by the iris 24. The plurality of rays 44 additionally comprisesan averaged ray 51 disposed between the paraxial ray 50 and the marginalray 52, for example, at a height at the pupil that is 1/√{square rootover (2)} or ½ times the height of the entrance pupil height. In someembodiments, the eye model additionally contains information regardingan object or source represented by the plurality of rays 44 entering theeye 20, for example, the distance of the source or object from the eye20 and/or the extent of the source or object in units of length or arclength.

Referring to FIG. 2 a, which is a magnified view of the region aroundretina 28, the rays 50-52 may come to focus at different points alongthe optical axis 28, which are labeled in the figure as marginal focus,best focus, and paraxial focus. As illustrated in the figure, thedistance between the marginal focus and the marginal focus may be usedto define a longitudinal spherical aberration (LSA). Such a result maybe produced, for example, when the surfaces of the IOL 30 are spherical.Alternatively, one or more of the surfaces of the IOL 30 may comprise anaspheric profile that is configured to reduce or eliminate sphericalaberrations produced either by an IOL made of spherical surfaces or byat least portions of the eye 20 (e.g., the cornea 22). In suchembodiments, as illustrated in FIG. 2 b, the rays 50-52 focus to acommon or substantially common point along the optical axis 28.

Embodiments of the invention may be used in conjunction with an eyemodel such as that illustrated in FIG. 1 to select or determine acharacteristic of an IOL to be implanted into the eye of a subject or aclass of subjects, for examples subjects of a particular age group orcondition (e.g., a class of subjects who have had a LASIK or similarprocedure). In certain embodiments, measurements from a subjects eye(e.g., AL, ACD, CR, LT) may be used in conjunction with statistical dataand/or an analytical tool (e.g., a ray trace program or algorithm) todetermine the characteristic of the IOL. The characteristic of the IOLresulting from embodiments of the invention may include the thickness ofthe IOL, the power of the IOL, the asphericity of the IOL, and/or thelocation of the IOL within the eye of the subject or subjects.

Referring to FIG. 3, in certain embodiments, a method 100 of selectingan IOL comprises one or more of the following operational blocks110-180. The method 100 comprises an operational block 110, whichcomprises determining physical characteristic of the eye such as anaxial eye length or a pupil size at a desired light level. The method100 further comprises an operational block 120, which comprisesdetermining a desired postoperative condition such as a postoperativerefraction and/or spherical aberration. The method 100 further comprisesan operational block 130, which comprises determining an asphericrepresentation of the corneal curvature or curvatures. The method 100also comprises an operational block 140, which comprises selecting anIOL with one or more predetermined characteristics (e.g., with apredetermined power or asphericity) and determining the location of aplane of fixation of the IOL following implantation (e.g., the lenshaptic plane or LHP). The method 100 additionally comprises anoperational block 150, which comprises employing the results ofoperational blocks 110-140 to establish an eye model. The method 100also comprises an operational block 160, which comprises computing, bymeans of an analytical tool (e.g., a ray tracing routine) with said eyemodel, an expected postoperative condition such as an expectedpostoperative refraction refraction and/or spherical aberration. Themethod 100 further comprises an operational block 170, which comprises,in the case the expected postoperative condition is not within thedesired postoperative condition, selecting another IOL with differentpower and/or asphericity and repeating operational blocks 150 and 160until the expected postoperative condition is within the desiredpostoperative condition. The method 100 may also comprise an operationalblock 180, which comprises selecting, for implantation, an implantableIOL of the nearest power and asphericity available or designing animplantable IOL that results in the desired postoperative refraction andspherical aberration.

The method 100 may also include transforming the measured axial lengthto a human population average scale by adding to the value atransformation constant. The axial length measured by ultrasound is notthe same as the optical axial length, and as the axial length measuredby one piece of equipment may differ from that measured by another one,there is a benefit to obtaining instrument independent measurements.Measurement of axial eye length for an individual patient may beobtained by ultrasound A-scan or the newer partial coherenceinterferometry (PCI) principle, available with the Zeiss IOLMaster.Regardless of the instrument and/or method used, the axial eye lengthmay first be transformed to a human population average (HPA) scale. Incertain embodiments, an underlying assumption for the HPA scale is thatthe mean axial length is about constant in any large group of adults.Transformation is discussed in more detail by Norrby et al. (J CataractRefract Surg 2003; 29:100-105) and the HPA scale is introduced by Norrbyet al. (J Cataract Refract Surg 2005; 31:1338-1344), both of which areherein incorporated by reference. Transformation amounts to the additionof a correction constant to the measured axial eye length. Thecorrection constant is generally regarded as instrument specific, forexample, as described in Norrby et al. (J Cataract Refract Surg 2005;31:1338-1344). A general outline of a routine to obtain a common scalefor axial lengths may include the following steps. First thepostoperative anterior chamber depth consistent with axial length,corneal radius, postoperative refraction and IOL power implanted arecalculated by thick lens ray tracing for a number of individual cases.The mean of the calculated anterior chamber depths may be calculated andcompared with a previous study with the same lens (e.g., PharmaciaCeeOn® 809C brand of IOL published in Koranyi et al.: J Cataract RefractSurg, 2002; 28:243-247, herein incorporated by reference). The measuredaxial lengths may then be transformed by addition of a constant value,and the mean anterior chamber depth was calculated anew. This processmay be iterated until the calculated mean anterior chamber depthcoincided with that of the other.

The pupil size may be measured preoperatively at the desired lightlevel, e.g. mesopic light (dusk). The pupil size at dusk is about 4 mm,but variations between at least about 2 mm to 6 mm or more can occur.

The aspheric representation of the anterior corneal is typically derivedfrom corneal topography, most commonly based on the so-called Placidodisk principle. Resulting height maps can be used to fit an asphericaldescription of the surface by a least squares optimization. Slit basedmethods such as implemented on the Orbscan® brand of topography systems(Bausch & Lomb) may be used for the same purpose (Holladay et al. JRefract Surg 2002; 18:683-691). The Orbscan® can also be used to obtainan aspherical description of the posterior corneal surface in the samemanner. Instruments based on the Scheimpflug principle, such as NidekEAS-100, may also be used to obtain anterior and posterior curvatures ofthe corneal surfaces. By rotating the slit and taking multiple picturesthe topography of both surfaces can be obtained. The newly presentedOculus Pentacam eye scanner, which is also based on the Scheimpflugprinciple, achieves this within a couple of arc seconds, and is suitablefor use with the method 100.

Independent of the measurement system used, the topography for thepurpose of the method 100 is conveniently described as a conicoidsurface of revolution, characterized by the aspheric constant k value(conic constant), optionally extended with additional polynomial terms.Preferably, k values are obtained for both anterior and posteriorcorneal surfaces, optionally in combination with additional polynomialterms.

The method 100 may be used to calculate an amount of at least one of apostoperative refraction and a postoperative spherical aberration for alens that is implantable into the eye of a subject. Preferably thecalculations are carried out using a ray tracing program or procedure,although other calculating means may also be used, such as an opticsdesign program. One benefit of the method 100 is that it is capable ofreducing the amount of computation necessary when using a ray tracingprocedure and yet produces reliable information for lens powerselection. Accordingly, only limited numbers of rays needs to beemployed with the routine rather than the great number of rays normallytraced for the purpose of optical design (several software packages arecommercially available, e.g., those sold under the brand names ofZemax®, OSLO®, Code V®), which are cumbersome to employ, although theycould be used for the purpose of the IOL power calculation andassessment of the resulting image quality.

In one aspect of the invention a ray entering the pupil at 1/√{squareroot over (2)} of the entrance pupil height is employed. This ray ishere termed the focusing ray. Alternatively a ray at the full pupildiameter (marginal ray) and a ray with close to zero ray height(paraxial ray) are traced. Focus is in this case assumed to be at themidpoint of the foci of the marginal and the paraxial rays. The distancebetween the foci of the marginal and the paraxial rays, the longitudinalspherical aberration (LSA), can also be used as a simple metric forimage quality. The smaller LSA is the better the image quality is.

According to one embodiment of the method 100, one or more of thesurfaces of an IOL such as the IOL 30 are described by the formula:

$\begin{matrix}{x = {\frac{\left( \frac{1}{R} \right)y^{2}}{1 + \sqrt{1 - {{k\left( \frac{1}{R} \right)}^{2}y^{2}}}} + {a_{4}y^{4}} + {a_{6}y^{6}} + \ldots}} & (1)\end{matrix}$wherein R is the radius of curvature at the apex, k the conic constant,y the radial distance from the optical axis and x the sag in thedirection of light propagation. Depending on the value of k the firstterm is a conic section and describes a:

-   -   hyperbola k<0    -   parabola k=0    -   prolate ellips 0<k<1    -   circle k=1    -   oblate ellips k>1

The coefficients for the additional polynomial terms a₄, a₆, etc. caneither be set to zero, in which case the surface is a conicoid ofrevolution, or be given positive or negative non-zero values to modifythe simple conic section rotational surface. Alternatively, the method100 may be used with other forms of the above equation or otherdefinitions of terms such as conic constant.

A method to design intraocular lenses for the purpose of correctingaverage corneal spherical aberration obtained from pooled corneal dataof a an elected patient group is further explained in the U.S. Pat. No.6,609,793, herein incorporated by reference. Corneas of the normalpopulation are in the prolate range (0<k<1) however, the method 100 isapplicable to all types of aspheric IOLs, such as IOLs with a hyperbolic(including parabolic) or oblate (including spherical) surfaces.

According to one aspect, patients having had corneal refractive surgeryto correct myopia can have a hyperbolic anterior surface (k≦0), whilethose having had corneal refractive surgery to correct hyperopia canhave an oblate anterior surface (k≧1) (Buehren et al., Scientific poster144, AAO 2004, New Orleans). The method 100 demonstrates satisfyingcapacity in obtaining careful prediction of IOL powers also for suchpatients, including estimating the resulting retinal image quality interms of LSA, although surfaces deviating considerably from prolate maybe required.

The method 100 may further comprise obtaining the corneal apex radius,typically both anterior and posterior corneal apex radii, from thetopography, or from corneal radius measured by conventional keratometry(at about 3 mm diameter) and corrected to the value at the apex by themethod described by Dubbelman et al. (Vision Res 2005; 45:117-132),herein incorporated by reference.

There are both indirect and direct methods available to preoperativelydetermine the location of the lens haptic plane (LHP), i.e. the distancefrom the anterior cornea to the LHP. Direct methods include ultrasoundbiomicroscopy, optical coherence tomography and Scheimpflug photographyas taught in U.S. Pat. No. 5,968,095, herein incorporated by reference.Newer, commercially available equipment having the capacity to conductsuch direct measurements includes the following systems, which areavailable from the listed companies: Artemis (Ultralink LLC), VisanteOCT (Zeiss), and Pentacam (Oculus).

Alternatively, the location of the lens haptic plane may be obtainedwith a prediction algorithm that includes preoperatively measuredparameters such as axial eye length (AL), corneal radius (CR) or,alternatively, corneal power (K), anterior chamber depth (ACD), andcrystalline lens thickness (LT). Norrby et al. (J Cataract Refract Surg2005; 31:1338-1344) have studied prediction algorithms of the generaltype:LHP=a+b×AL+c×ACD+d×LT+e×CR+f×AL ² +g×ACD ² +h×LT ² +i×CR ²+j×AL×ACD+k×AL×LT+l×AL×CR+m×ACD×LT+n×ACD×CR+o×LT×CR  (2)

One finding of the study mentioned is that AL and ACD measured with onepiece of equipment can deviate systematically from that measured withanother piece of equipment (Norrby et al. J Cataract Refract Surg 2003;29:95-99; see also Koranyi et al. J Cataract Refract Surg 2002;28:243-247, and Norrby, J Cataract Refract Surg 2001; 27:1656-1661, allof which are herein incorporated by reference). To correct measured ALand ACD the concept of a Human Population Average (HPA) scale wasdevised (Norrby et al. J Cataract Refract Surg 2005; 31:1338-1344).Algorithms containing LT and ACD in general were found to be unreliablewhen employing measurements obtained with different pieces of equipment,despite correction of ACD to the HPA scale (Norrby et al. J CataractRefract Surg 2005; 31:1338-1344). Also the early attempts to model LHPin terms of and LT and ACD (Norrby and Koranyi, J Cataract Refract Surg1997; 23:254-259, U.S. Pat. No. 5,968,095, both of which are hereinincorporated by reference) were found unreliable. Regression formulascontaining CR and AL in linear, quadratic and cross-terms, with orwithout the constant a, in accordance with the general formula above,gave consistent results independent of the measurement equipment used,when AL was transformed to the HPA scale. A preferred algorithm isLHP=2.486+0.2174×(AL+ΔAL)−0.4213×CR  (3)wherein AL is the measured axial eye length, ΔAL is the transformationconstant (ranging from 0.2 mm to 1.0 mm depending on equipment used) andCR is the keratometric corneal radius (at about 3 mm diameter); (seealso S Norrby et al. J Cataract Refract Surg 2005; 31:1338-1344). Theposition of the IOL 30 in the eye is determined by its vault height,i.e. the distance between the LHP and the anterior apex of the IOL 30,where the LHP coincides with the plane of contact between the IOLhaptics and ocular tissue (e.g. the capsular bag). The vault height isconsidered to be positive if the anterior IOL apex is posterior to LHPand negative if the anterior IOL apex is anterior to LHP.

The present invention also relates to an improved eye model, whichadmits simple ray tracing procedures to evaluate suitable intraocularlenses for implantation and to select a lens available in terms ofrefractive power and/or asphericity. The eye model includes values ofthe axial eye length based on a measured axial eye length transformed tothe human population average scale by addition of a transformationconstant; the pupil size at a desired light level, an asphericrepresentation of the corneal curvature and a value of the lens hapticplane location (the plane of fixation of an implantable IOL followingimplantation). Routines of how to obtain the mentioned necessary valuesfor the eye model from an individual are described above. Besidesadmitting a significant calculation simplicity, the invented eye modelprovides estimations that are substantially independent from what typeof biometric instrumentation that are used for the eye axial length.

In certain embodiments, a method comprises determining the opticalquality of an eye following the implantation of an implantable IOL. Themethod may be based upon using the above described eye model with anaspheric IOL and a ray tracing routine, for example, in which a marginalray and a paraxial ray are used to calculate the longitudinal sphericalaberration (LSA). If an undesired high value of LSA is obtained from themethod, another lens with another power and/or asphericity is selectedand the method is repeated until a lens is found that provides apredetermined optical quality, as represented by a low LSA.

Referring to FIG. 4, in certain embodiments, a method 200 of selectingan IOL comprises one or more of the following operational blocks210-270. Where appropriate, aspects of the method 100 discussed aboveherein may also be applied to embodiments of the method 200. The method200 comprises an operational block 210, which comprises determining oneor more ocular dimensions based on one or more measurements of at leastone eye. The method 200 also comprises an operational block 220, whichcomprises selecting a desired refractive outcome. The method 200comprises an operational block 230, which comprises selecting an IOL(e.g., the IOL 30) having at least one of a power, an aspheric profile,and a lens plane. The method 200 comprises an operational block 240,which comprises establishing an eye model based on one or morecharacteristics of the at least one eye. The method 200 comprises anoperational block 250, which comprises determining a location of thelens plane. The method 200 comprises an operational block 260, whichcomprises performing a calculation to determine a predicted refractiveoutcome based on the eye model and a ray tracing algorithm. The method200 comprises an operational block 270, which comprises comparing thepredicted refractive outcome to the desired refractive outcome. Themethod 200 comprises an operational block 280, which comprises, based onthe comparison, repeating the calculation with an IOL having at leastone of a different power, a different aspheric profile, and a differentlens plane. The method 200 comprises an operational block 290, whichcomprises selecting an implantable IOL configured for implantation intothe eye of a subject.

Referring to operational block 210, the method 200 incorporate one ormore ocular dimensions based, for example, the eye model illustrated inFIG. 1. In certain embodiments, the method 200 may incorporate data froma database of eyes or from a plurality of eyes belonging to subjectbelonging to a particular population such as a population of cataractpatients or subjects that have received a corneal treatment for visioncorrection. Such data is illustrated, for instance, in U.S. Pat. Nos.6,609,793 and 6,830,332 and U.S. Patent Application Publication2004/088050, all herein incorporated by reference.

Referring to operational block 220, the desired refractive outcome maybe, for example, providing a subject with distant vision and/or nearvision. This may include providing the subject sufficient visual acuitythat there is no need for external corrective spectacles or contactlenses for near and/or distant vision. Alternatively, the refractiveoutcome may be less stringent in terms of the degree of correction. Forexample the refractive outcome might to provide sufficient visual acuitysuch that normal vision is provided by the use of external correctivespectacles or contact lenses having a correction of less than about 3Diopters, preferably less than 2 Diopters, and more preferably less than1 Diopter. In some embodiments the desired refractive outcome isreduction of spherical aberrations or other higher order aberrationsthat would have been created by the use of, for example, and IOL havingonly spherical surfaces. Alternatively or additionally, the desiredrefractive outcome is reduction of spherical aberrations or other higherorder aberrations induced by the cornea or some other part of the eye.Such criteria are discussed in U.S. Pat. No. 6,609,793.

Referring to operational block 250, the lens plane may be lens hapticplane (LHP) illustrated, for example, in FIG. 1. Alternatively, the lensplane may be some other that is appropriate for determining, forexample, the power, asphericity, and/or location of an IOL in within theeye of a subject. For example, the lens plane used in the method 200 maybe an effective principal plane of the optic 32. In such embodiments, adistinction may be made between lenses of various manufactures so thateffect of different geometries on IOL performance may be taken intoaccount.

Referring to operational block 260, calculation of a predictedrefractive outcome is based not simply on measurements and correlationdatabases, such as those used in currently existing formulas such asHolladay 1 and 2, Hoffer Q, and SRK/T and a ray tracing algorithm.Rather, the current method 200 calculates a predicted refractive outcomebased on a ray tracing or wavefront analysis in addition to usingmeasurement and correlation databases. This approach has been found bythe inventor to provide a more reliable way of providing a patient alens with the correction power to provide normal vision as well asprovide the possibility of correcting for higher order ocularaberrations such as spherical aberrations. The one or more oculardimensions may include, for example, any of the dimension of any of theelements of the eye 20 illustrated in FIG. 1

In certain embodiments, a computer system 300 for selecting an IOL forplacement into the eye of a subject comprises a processor 302 and acomputer readable memory 304 coupled to the processor 302. The computerreadable memory 304 has stored therein an array of ordered values 308and sequences of instructions 310 which, when executed by the processor302, cause the processor 302 to select an implantable IOL configured forimplantation into the eye of a subject. The array of ordered values 308may comprise data used or obtained from the methods 100, 200 or othermethods consistent with embodiments of the invention. For example, thearray of ordered values 308 may comprise one or more ocular dimensionsof an eye or plurality of eyes from a database, a desired refractiveoutcome, parameters of an eye model based on one or more characteristicsof at least one eye, and data related to an IOL or set of IOLs such as apower, an aspheric profile, and/or a lens plane. The sequence ofinstructions 310 may include one or more steps of the methods 100, 200or other methods consistent with embodiments of the invention. In someembodiments, the sequence of instructions 310 includes determining alocation of the lens plane of an IOL, performing one or morecalculations to determine a predicted refractive outcome based on an eyemodel and a ray tracing algorithm, comparing a predicted refractiveoutcome to a desired refractive outcome, and based on the comparison,repeating the calculation with an IOL having at least one of a differentpower, a different aspheric profile, and a different lens plane.

The computer system 300 may be a general purpose desktop or laptopcomputer or may comprise hardware specifically configured performing thetask of selecting an IOL for placement into the eye of a subject. Insome embodiments, the computer system 300 is configured to beelectronically coupled to another device such as a phacoemulsificationconsole or one or more instruments for obtaining measurements of an eyeor a plurality of eyes. In other embodiments, the computer system 300 isa handheld device that may be adapted to be electronically coupled toone of the devices just listed.

A number of examples will now be presented demonstrating how methods anddevices according to embodiments of the invention may be used todetermine a suitable lens for a patient in terms refractive power and/orreduced aberrations. These examples also demonstrate that these methodscan be used to estimate the visual quality of the patient in terms ofthe longitudinal spherical aberration (LSA) of the retinal image. Theexamples given demonstrate that methods according to the invention areapplicable for different k values of the cornea and the importance ofconsidering pupil size and how consideration of k values for bothanterior and posterior corneal surfaces effect the predictability of themethods.

Example 1 Demonstration of the Ray Tracing Technique for the FocusingRay

In this and the following examples, a ray tracing procedure is used indetermining various lens parameters such as, for example, IOL opticpower and LHP. The ray tracing procedure utilized is in the form of aMicrosoft Excel spreadsheet; however, any ray tracing program or routinemay, in general, be utilized in various embodiments of the invention. Inthe ray tracing discussed here, a meridional ray impinges on a surfaceand follows a straight line, as expressed byy=y _(o) +ut  (4)where y_(o) is the radial height at the origin, u the angle (in radians)between the ray and the optical axis and t the distance, along andparallel with the optical axis, between the origin and the intersectionwith the surface.

The condition for intersection is that the radial height y at thesurface and of the ray is the same. The calculation can be set up in anExcel spreadsheet and the Goal Seek (or Solver) utility can be used tofind the value for t for which there is zero difference between theheights of the surface and of the ray. In this examples, the additionalpolynomial terms (a₄y⁴,a₆y⁶) are set equal to zero for simplicity, butthe method is valid for non-zero values also.

The slope of the surface at the point of intersection is found bynumeric differentiation. From the slope, the angle of the normal isfound, and Snell's law of refraction is applied to find the angle of therefracted beam. The intersection of the refracted beam with next surfaceis sought as before, the slope at the point of intersection is found asbefore, Snell's law of refraction is again applied to find the angle ofthe beam leaving this surface, etc. until after refraction at the lastsurface the intersection between that beam and the optical axis (focus)is sought. This calculation can be set up as a macro program to performthese calculations.

A ray traced at 1/√{square root over (2)}≈0.7 of the height of theentrance pupil height is an average ray in the sense that it divides thepupil into two surfaces of equal area, one outer annular ring and acentral circle. It is here termed the focusing ray and its intersectionwith the optical axis is adopted as one definition of best focus.

An alternative definition of best focus is the midpoint between amarginal ray (i.e. a ray entering at the margin of the pupil) and aparaxial ray (i.e. entering infinitesimally close to the optical axis atthe pupil). The distance between the foci of the marginal and paraxialrays, the longitudinal spherical aberration (LSA) is a simple metric foroptical quality of the image formed at the photoreceptor layer of theretina. The sign convention is here taken that if the paraxial rayfocuses posterior to the marginal ray, the spherical aberration istermed positive. Conversely if the paraxial ray focuses anterior to themarginal ray, the spherical aberration is negative. The best imagequality is when LSA is zero. The smaller the absolute value of LSA, thebetter the image quality.

The entrance pupil (on the first spectacle lens surface) is 5 mm in thisexample.

CORNEA Surface Apex radius (mm) k anterior 7.7 0.82 posterior 6.8 0.66

LENS Surface Apex radius (mm) k anterior 12.154 −5 posterior −12.154 −5

Coefficients a₄, a₆, etc. are all set equal to zero in this example.

AXIAL DISTANCES Object Spectacle Vertex Corneal Anterior IntraocularAxial Transf. distance lens thickness distance thickness chamber depthlens thickness length const. 6 m 2 mm 12 mm 0.5 mm 4.9 mm 1.13 mm 23.77mm 0.23 mm

Anterior chamber depth is defined here and in subsequent examples as thedistance from the anterior apex of the cornea to the anterior apex ofthe lens (whether the natural lens or an IOL). The transformationconstant, here assumed to be 0.23, transforms the measured axial lengthto the human population average (HPA) scale.

REFRACTIVE INDICES Spectacle Intraocular Air lens Cornea Aqueous lensVitreous 1 1.5 1.376 1.336 1.458 1.336

The macro program “Sub trace( )” is run to determine the ray path withthe given input, followed by “Sub spectacle( )” to find the spectaclepower giving zero ray height at the retina, i.e. the power to focus theimage on the photoreceptor layer of the retina. Because changing thespectacle power changes the ray incidence on the cornea, “Sub trace( )”is run again followed by “Sub spectacle( )”. Repeating this sequence afew times results in sufficient accuracy in the final result.

FIG. 6 illustrates the formulas programmed into each cell of the Excelspreadsheet used to provide the ray tracing program, while FIG. 7illustrates the numerical result of the calculation in each cell. TheSub trace( ) and Sub spectacle( ) routines used in the spreadsheet modelare as follows:

Sub trace( ) Range(“D12”).GoalSeek Goal:=0, ChangingCell:=Range(“D10”)Range(“E12”).GoalSeek Goal:=0, ChangingCell:=Range(“E10”)Range(“F12”).GoalSeek Goal:=0, ChangingCell:=Range(“F10”)Range(“G12”).GoalSeek Goal:=0, ChangingCell:=Range(“G10”)Range(“H12”).GoalSeek Goal:=0, ChangingCell:=Range(“H10”)Range(“I12”).GoalSeek Goal:=0, ChangingCell:=Range(“I10”)Range(“J12”).GoalSeek Goal:=0, ChangingCell:=Range(“J10”) End Sub

Sub spectacle( ) Range(“J8”).GoalSeek Goal:=0, ChangingCell:=Range(“D4”)End Sub

In the example, the spectacle power becomes +0.01 D. FIG. 8.

Example 2 Selecting Power of a Spherical IOL

The entrance pupil (on the first spectacle lens surface) is 5 mm in thisexample.

CORNEA Surface Apex radius (mm) k anterior 7.87 0.82 posterior 6.40 0.66

The radii apply at the center of the cornea. Corneal radius determinedwith a keratometer applies at a circle of about 3 mm diameter. With thek-values given, 7.90 mm and 6.42 mm, respectively, would have beenmeasured.

INTRAOCULAR LENSES Power Front radius Back radius Thickness Vault height(D) (mm) (mm) (mm) (mm) 20.0 12.154 −12.154 1.10 0.03 20.5 11.856−11.856 1.11 0.03 21.0 11.572 −11.572 1.12 0.02

Vault height is the distance from LHP to the anterior surface of thelens (positive if the lens surface is posterior to LHP).

AXIAL DISTANCES Object Spectacle lens Vertex Corneal Axial distancethickness distance thickness LHP length 6 m 2 mm 12 mm 0.574 mm 4.36 mm23.92 mm

LHP was calculated by the formulaLHP=2.486+0.2174×(AL+ΔAL)−0.4213×CR

where CR is the measured corneal radius (7.90 mm), AL is the measuredaxial length (23.69 mm) and ΔAL is the transformation constant, hereassumed to be 0.23 mm (AL+ΔAL) is the axial length transformed to thehuman population average (HPA) scale, which is the value given in thetable. The anterior chamber depth is LHP plus the vault height for thespecific IOL chosen.

REFRACTIVE INDICES Spectacle Intraocular Air lens Cornea Aqueous lensVitreous 1 1.5 1.376 1.336 1.458 1.336

RESULTS IOL (D) Spectacle (D) 20.0 +0.40 20.5 +0.03 21.0 −0.37

A surgeon would probably choose to implant the 21.0 D lens. Slightmyopia is often preferred.

Using the midpoint between marginal and paraxial ray foci as focusingcriterion the following results are obtained.

RESULTS IOL (D) Spectacle (D) 20.0 +0.39 20.5 +0.01 21.0 −0.38

These results are for all practical purpose equal to those obtained withthe focusing ray as focusing criterion. The axial defocus of themarginal and paraxial rays in relation to the focusing rays are given inthe following table.

DEFOCUS IN RELATION TO FOCUSING RAY IOL (D) Marginal ray Paraxial ray20.0 −0.267 +0.259 20.5 −0.278 +0.268 21.0 −0.289 +0.279

The marginal ray thus focuses anterior and the paraxial ray posterior tothe focusing ray, indicating that the optical system has overallpositive spherical aberration. The near symmetry in relation to thefocusing ray is another indication of the agreement between the twofocusing criteria in this example.

Example 3 Selecting Power of an Aspherical IOL

A generalized aspheric surface may be characterized using Equation (1),discussed in greater detail above herein. The entrance pupil (on thefirst spectacle lens surface) is 5 mm in this example.

CORNEA Surface Apex radius (mm) k anterior 7.87 0.82 posterior 6.40 0.66

The radii apply at the center of the cornea. Corneal radius determinedwith a keratometer applies at a circle of about 3 mm diameter. With thek-values given, 7.90 mm and 6.42 mm, respectively, would have beenmeasured.

INTRAOCULAR LENSES Anterior surface Posterior surface Thick- Vault PowerRadius Radius ness height (D) (mm) k (mm) k (mm) (mm) 20.0 12.154 −7−12.154 −7 1.13 0.01 20.5 11.856 −11.856 1.13 0.00 21.0 11.572 −11.5721.14 0.00 21.5 11.301 −11.301 1.15 −0.01 22.0 11.043 −11.043 1.16 −0.01

Vault height is the distance from LHP to the anterior surface of thelens.

AXIAL DISTANCES Object Spectacle lens Vertex Corneal Axial distancethickness distance thickness LHP length 6 m 2 mm 12 mm 0.574 mm 4.36 mm23.92 mm

LHP was calculated by the formula,LHP=2.486+0.2174×(AL+ΔAL)−0.4213×CR,where CR is the measured corneal radius (7.90 mm), AL is the measuredaxial length (23.69 mm) and ΔAL is the transformation constant, hereassumed to be 0.23 mm (AL+ΔAL) is the axial length transformed to thehuman population average (HPA) scale, which is the value given in thetable. The anterior chamber depth is LHP plus the vault height for thespecific IOL chosen.

REFRACTIVE INDICES Spectacle Intraocular Air lens Cornea Aqueous lensVitreous 1 1.5 1.376 1.336 1.458 1.336

RESULTS IOL (D) Spectacle (D) 20.0 +1.19 20.5 +0.87 21.0 +0.57 21.5+0.26 22.0 −0.04

Using the midpoint between marginal and paraxial ray foci as focusingcriterion, the expected spectacle refraction is −0.11 D with the 22.0 DIOL. The focus of the marginal ray is +0.067 mm in relation to thefocusing ray, i.e. focuses posterior to the focusing ray. The focus ofthe paraxial ray is −0.118 mm in relation to the focusing ray, i.e.focuses anterior to the focusing ray. This system thus exhibits negativespherical aberration, reversing the focusing order of the rays.

Example 4 Demonstrating the Influence of k-Value

The entrance pupil (on the first spectacle lens surface) is 5 mm in thisexample.

The average k-value in the human population is 0.82, with a standarddeviation of 0.18 (Dubbelman, M., Weeber, H. A., van der Heijde, G. L.and Völker-Dieben, H. J. Radius and asphericity of the posterior cornealsurface determined by corrected Scheimpflug photography. Acta OphthalmolScand 2002; 80: 379-383).

For illustration a 20.5 D spherical lens and a 21.5 D aspherical lenswith the following designs are chosen.

INTRAOCULAR LENSES Anterior surface Posterior surface Thick- Vault PowerRadius a₄ a₆ Radius a₄ a₆ ness height (D) (mm) k (mm⁻⁴) (mm⁻⁶) (mm) k(mm⁻⁴) (mm⁻⁶) (mm) (mm) 20.5 11.856 1 0 0 −11.856 1 0 0 1.11 0.03spherical 21.5 11.301 −4 −1 · 10⁻⁴ −1 · 10⁻⁶ −11.301 −4 0 0 1.15 −0.01aspherical

Assume that the surgeon has come to these lens powers with a calculationmethod that does not take corneal asphericity into account. Whichinfluence will variation of up to 3 standard deviations of cornealasphericity have on postoperative refraction?

The keratometrically (at 3 mm diameter) measured anterior corneal radiusis assumed to be 7.90 mm. The posterior radius is unknown, but is as inprevious examples assumed to be 6.42 mm (at 3 mm diameter) and have ak-value of 0.66. The shape of the posterior surface is further assumedto be independent of that of the anterior surface and remain unchangedwhen the k-value of the anterior surface is varied.

ANTERIOR CORNEAL SURFACE Surface characteristics Apex ±SD k type radius(mm) −3 0.28 prolate 7.79 −2 0.46 prolate 7.82 −1 0.64 prolate 7.84 ±00.82 prolate 7.87 +1 1.00 sphere 7.90 +2 1.18 oblate 7.92 +3 1.36 oblate7.95

AXIAL DISTANCES Axial Spectacle length Object lens Vertex Corneal(trans- distance thickness distance thickness LHP formed) 6 m 2 mm 12 mm0.574 mm 4.36 mm 23.92 mm

REFRACTIVE INDICES Spectacle Intraocular Air lens Cornea Aqueous lensVitreous 1 1.5 1.376 1.336 1.458 1.336

RESULTS Spectacle correction (D) with Spherical Aspherical IOL IOL SD k20.5D 21.5D −3 −0.72 0.21 0.23 −2 −0.54 0.15 0.15 −1 −0.36 0.09 0.07 ±0−0.18 0.03 −0.01 +1 0.00 −0.04 −0.10 +2 0.18 −0.10 −0.18 +3 0.36 −0.17−0.27

This example shows that the effect of neglecting corneal asphericity inIOL power calculation has effect on the postoperative refraction forspherical as well as for aspherical IOLs.

Example 5 Finding the Influence of Pupil Size

The entrance pupil is defined on the first spectacle lens surface and isvaried in this example.

For this example a 20.5 D spherical lens and a 21.5 D aspherical lenswith the following designs are chosen.

INTRAOCULAR LENSES Anterior surface Posterior surface Thick- Vault PowerRadius a₄ a₆ Radius a₄ a₆ ness height (D) (mm) k (mm⁻⁴) (mm⁻⁶) (mm) k(mm⁻⁴) (mm⁻⁶) (mm) (mm) 20.5 11.856 1 0 0 −11.856 1 0 0 1.11 0.03spherical 21.5 11.301 0 −1 · 10⁻³ 1 · 10⁻⁶ −11.301 1 0 0 1.15 −0.01aspherical

Normally pupil size is not considered in IOL power calculation. About 4mm is common at mesopic light conditions (dusk), but individualvariations from 2 mm up to 6 mm or even wider are known. What could theconsequences be for patients depending on pupil size?

The following additional parameters are assumed.

CORNEA Apex radius Surface (mm) k anterior 7.87 0.82 posterior 6.40 0.66

AXIAL DISTANCES Spectacle Axial Object lens Vertex Corneal length(trans- distance thickness distance thickness LHP formed) 6 m 2 mm 12 mm0.574 mm 4.36 mm 23.92 mm

REFRACTIVE INDICES Spectacle Intraocular Air lens Cornea Aqueous lensVitreous 1 1.5 1.376 1.336 1.458 1.336

RESULTS Postoperative refraction (D) with Spherical Aspherical Pupil IOLIOL (mm) 20.5D 21.5D 2 +0.62 +0.02 3 +0.49 +0.06 4 +0.29 +0.10 5 +0.03+0.15 6 −0.32 +0.20

This example shows that the pupil size can have large effects onpostoperative refraction, in particular in an eye with much sphericalaberration, i.e. in the normal case an eye with a spherical IOL. Theaspherical IOL in this example corrects for most of the sphericalaberration of the cornea, but not all, hence there is some effect ofpupil size on postoperative refraction. However, if the cornealaberrations were perfectly corrected by the IOL, there would be noeffect of pupil size on postoperative refraction.

Example 6 Consequence of not Knowing the Posterior Corneal Curvature

The entrance pupil (on the first spectacle lens surface) is 5 mm in thisexample.

For this example a 20.5 D spherical lens and a 22.0 D aspherical lenswith the following designs are chosen.

INTRAOCULAR LENSES Anterior surface Posterior surface Thick- Vault Powerradius radius ness height (D) (mm) k (mm) k (mm) (mm) 20.5 11.856 1−11.856 1 1.11 0.03 spherical 22.0 11.043 −7 −11.043 −7 1.16 −0.01aspherical

Coefficients a₄, a₆, etc. are all set equal to zero in this example.

In the normal case only the anterior radius of the cornea is measured,known and used in IOL power calculation. Corneal thickness, posteriorradius and posterior asphericity is generally not known. What are theconsequences of making assumptions about these unknown quantities?

Assume as before that the corneal curvature (at 3 mm) measured bykeratometry was found to be 7.90 mm.

CORNEAL CASES Anterior surface Posterior surface Apex Apex Thick- Ratioof radii radius radius ness (posterior/ (mm) k (mm) k (mm) anterior Case1 7.87 0.82 6.40 0.66 0.574 0.81 Case 2 7.87 0.82 6.40 1.00 0.574 0.81Case 3 7.87 0.82 7.30 0.82 0.574 0.93 Case 4 7.87 0.82 6.40 0.66 0.0000.81 Case 5 7.87 0.82 6.95 1.00 0.574 0.88 Case 6 7.87 1.00 6.40 1.000.574 0.81

Case 1 is considered to have the proper values for all variables. Theratio of radii is taken from Dubbelman et al. Acta Ophthalmol Scand2002; 80:379-383. In Case 2 the posterior surface is assumed to bespherical. In Case 3 the posterior surface is assumed to be concentricwith the anterior surface and having the same asphericity, which leadsto the ratio of radii given. In Case 4 the corneal thickness isneglected. In Case 5 the ratio of radii is assumed to follow the classicGullstrand model, i.e. 6.8/7.7. In Case 6 both surfaces are assumedspherical.

The following additional parameters are assumed.

AXIAL DISTANCES Object Spectacle lens Vertex Corneal Axial lengthdistance thickness distance thickness (transformed) 6 m 2 mm 12 mm 0.574mm 23.92 mm

REFRACTIVE INDICES Spectacle Intraocular Air lens Cornea Aqueous lensVitreous 1 1.5 1.376 1.336 1.458 1.336

RESULTS Postoperative refraction (D) with Spherical Aspherical IOL IOL20.5D 22.0D Case 1 +0.03 −0.04 Case 2 +0.11 +0.04 Case 3 −0.74 −0.78Case 4 +0.25 +0.18 Case 5 −0.42 −0.47 Case 6 +0.04 +0.03

Whether the IOL is spherical or aspherical this example shows that theposterior corneal radius, i.e. the assumed ratio of radii, has thelargest influence (Cases 3 and 5). Putting corneal thickness equal tozero (Case 4) causes less than a quarter of dioptre increase inrefraction. Neglecting posterior corneal asphericity (Case 2) has littleinfluence, and simultaneously disregarding asphericity of both surfaces(Case 6) has close to negligible influence. This result is coincidentalthough. Other initial asphericities would give different results as canbe inferred from Example 4.

Example 7 Alternative Calculations Using Optical Design Programs

The entrance pupil (on the first spectacle lens surface) is 5 mm in thisexample.

For illustration a 20.5 D spherical lens and a 22.0 D aspherical lenswith the following designs are chosen.

INTRAOCULAR LENSES Anterior Posterior surface surface Power radiusradius Thickness (D) (mm) k (mm) k (mm) 20.5 11.856 1 −11.856 1 1.11spherical 22.0 11.043 −7 −11.043 −7 1.16 aspherical

Using the optical design software OSLO alternative focusing criteriawere evaluated

-   -   Minimum on-axis spot size    -   Minimum RMS OPD on axis    -   Maximum MTF at 20 cycles/mm    -   Maximum MTF at 50 cycles/mm

Calculations are monochromatic assuming the following refractiveindices.

REFRACTIVE INDICES Spectacle Intraocular Air lens Cornea Aqueous lensVitreous 1 1.5 1.376 1.336 1.458 1.336

The keratometrically (at 3 mm diameter) measured anterior corneal radiusis assumed to be 7.90 mm. The posterior radius is unknown, but is as inprevious examples assumed to be 6.42 mm (at 3 mm diameter) and have ak-value of 0.66. The apex radii are slightly steeper due to theasphericity.

CORNEA Apex radius Surface (mm) k anterior 7.87 0.82 posterior 6.40 0.66

Other parameters are as follows.

AXIAL DISTANCES Object Spectacle Vertex Corneal Aqueous Vitreousdistance lens thickness distance thickness thickness thickness IOL type(m) (mm) (mm) (mm) (mm) (mm) Spherical 6 2 12 0.574 3.811 18.425Aspherical 3.771 18.415

Vitreous thickness includes an assumed 0.25 mm retinal thickness.

RESULTS Spectacle power (D) with Spherical IOL Aspherical IOL FOCUSINGof 20.5D of 22.0D CRITERION power power Minimum spot size −0.27 +0.03Minimum RMS OPD −0.01 −0.05 Max MTF @ 20 c/mm −0.16 +0.01 Max MTF @ 50c/mm +0.26 −0.01 Focusing ray +0.03 −0.04

It can be seen that the Minimum RMS OPD criterion, which is a commonlyaccepted definition of best focus, agrees well with the focusing ray forboth the spherical and the aspherical IOLs. The considerable amount ofspherical aberration in case of the spherical IOL causes the variousfocusing criteria to disagree.

The through-focus MTF plots (output by the OSLO program) at 20 and 50cyc/mm used to determine maximum MTF are shown in FIGS. 9A-9D. Thehorizontal line at the top is the diffraction limited MTF of the systemat the spatial frequency given.

Example 8 Correcting Extreme Corneal Aberrations by Adjusting the Shapeof the IOL

The entrance pupil (on the first spectacle lens surface) is 4 mm in thisexample.

The k-value can vary considerably outside the normal range (see Example4) in persons who have undergone corneal refractive surgery. Correctionof myopia tends to make the corneal spherical aberration more positive(towards oblate), while correction of hyperopia tends to make thecorneal spherical aberration more negative (towards hyperopic) (Buehrenet al., Scientific poster 144, AAO 2004, New Orleans).

Consider two eyes, one originally −5 D axially myopic and the other +5 Daxially hyperopic. They thus differ in axial length and proportionallyin anterior chamber depth. However, their corneas and lenses areoriginally assumed to be identical. Their refractive state ischaracterized by the spectacle spherical equivalent (SE) andlongitudinal spherical aberration (LSA). The anterior chamber depth wasestimated from clinical data for eyes of corresponding lengths.

For this example the following refractive indices are assumed.

REFRACTIVE INDICES Spectacle Aqueous, Crystalline Intraocular Air lensCornea vitreous lens lens 1 1.5 1.376 1.336 1.4274 1.458

The eyes can now be summarized as follows.

ORIGINAL STATUS OF THE EYES Cornea Crystalline lens Anterior PosteriorAnterior Posterior Refractive state Apex Apex Thick- Apex Apex Thick-Ocular distances Original SE LSA radius radius ness radius radius nessAL ACD LHP ametropia (D) (mm) (mm) k (mm) k (mm) (mm) k (mm) k (mm) (mm)(mm) (mm) Myopic −5.0 0.084 7.870 0.82 6.400 0.66 0.574 10.670 −3 −5.848−2 3.76 25.43 3.47 4.74 Hyperopic +5.0 0.023 7.870 0.82 6.400 0.66 0.57410.670 −3 −5.848 −2 3.76 21.62 2.96 3.91

LHP was calculated from the formulaLHP=2.486+0.2174×(AL+ΔAL)−0.4213×CR

in which the transformation constant ΔAL was set to 0.25 mm and thecorneal radius at 3 mm CR is 7.896 mm with the apex radius and k-valueas given in the table.

Assume that these eyes undergo corneal refractive surgery to make thememmetropic. Besides correcting the spherical equivalent the myopic eyeis assumed to become one unit of k-value towards oblate, and thehyperopic eye is assumed to become one unit of k-value towardshyperopic. The myopic correction further results in decrease of thecentral thickness of the cornea amounting to 0.060 mm, while thehyperopic correction does not cause any change of the central thicknessof the cornea. The decrease in corneal thickness causes a correspondingdecrease in AL, ACD and LHP in the myopic case. The following situationensues.

STATUS OF THE EYES AFTER CORNEAL REFRACTIVE SURGERY Cornea Crystallinelens Refractive state Apex Apex Thick- Apex Apex Thick- Ocular distancesOriginal SE LSA radius radius ness radius radius ness AL ACD LHPametropia (D) (mm) (mm) k (mm) k (mm) (mm) k (mm) k (mm) (mm) (mm) (mm)Myopic 0.00 0.434 8.794 1.82 6.400 0.66 0.514 10.670 −3 −5.848 −2 3.7625.37 3.41 4.68 Hyperopic 0.00 −0.522 6.967 −0.18 6.400 0.66 0.57410.670 −3 −5.848 −2 3.76 21.62 2.96 3.91

Note that the myopic eye now has considerable positive sphericalaberration (LSA) and that the surgery of the hyperopic has even reversedthe sign and resulted in considerable negative spherical aberration(LSA) of the entire eye.

Assume that these eyes several years later are eligible for cataractsurgery. The aim of the surgery is emmetropia (with the target at 6 m)and elimination of spherical aberration. The following lenses aredesigned for this purpose.

IOL Vault Anterior surface Posterior surface Original Power Thicknessheight radius a4 A6 radius a4 a6 ametropia (D) (mm) (mm) (mm) k (mm⁻⁴)(mm⁻⁶) (mm) k (mm⁻⁴) (mm⁻⁶) Myopic 23.20 1.19 −0.02 10.468 −5.45 −1.00 ·10⁻³ −4.85 · 10⁻⁵ −10.468 1 0 0 Hyperopic 20.23 1.13 0.00 12.012 2.45 8.80 · 10⁻⁴ −1.40 · 10⁻⁵ −12.012 1 0 0

The situation is now characterized as follows.

STATUS OF THE EYES AFTER CATARACT SURGERY Cornea Anterior PosteriorRefractive state Apex Apex Thick- Ocular distances Original SE LSAradius radius ness AL ACD LHP ametropia (D) (mm) (mm) k (mm) k (mm) (mm)(mm) (mm) Myopic 0.00 0.00 8.794 1.82 6.400 0.66 0.514 25.37 4.66 4.68Hyperopic 0.00 0.00 6.967 −0.18 6.400 0.66 0.574 21.62 3.91 3.91

This example shows that intraocular lenses can be designed to correctrotationally symmetrical aberrations, i.e. sphere and sphericalaberration, for eyes having extreme corneal spherical aberration.

The above presents a description of the best mode contemplated ofcarrying out the present invention, and of the manner and process ofmaking and using it, in such full, clear, concise, and exact terms as toenable any person skilled in the art to which it pertains to make anduse this invention. This invention is, however, susceptible tomodifications and alternate constructions from that discussed abovewhich are fully equivalent. Consequently, it is not the intention tolimit this invention to the particular embodiments disclosed. On thecontrary, the intention is to cover modifications and alternateconstructions coming within the spirit and scope of the invention asgenerally expressed by the following claims, which particularly pointout and distinctly claim the subject matter of the invention.

What is claimed is:
 1. A method of selecting an IOL to be implanted inthe eye of a subject comprising: a) determining an axial eye length anda pupil size at a desired light level and determining at least one of adesired postoperative refraction and a desired postoperative sphericalaberration; b) determining an aspheric representation of a cornealcurvature; c) selecting an IOL with predetermined power and asphericity,and determining a location of the lens haptic plane (LHP); d) employingthe results of previous sections to establish an eye model for the eyeof the subject, the eye model including the axial eye length, the pupilsize, the aspheric representation of the corneal curvature, and the LHP;e) computing with a ray tracing routine and the axial eye length, thepupil size, the aspheric representation of the corneal curvature, andthe LHP of said eye model, an expected at least one of a postoperativerefraction and postoperative spherical aberration; f) in the case thatthe at least one of the expected postoperative refraction andpostoperative spherical aberration is not within a predeterminedcriteria, selecting another IOL with different power and/or asphericityand repeating steps d) and e) until the at least one of the expectedpostoperative refraction and postoperative spherical aberrations iswithin the at least one of the desired postoperative refraction anddesired postoperative spherical aberration; and g) selecting, forimplantation, an implantable IOL of the nearest power and asphericityavailable.
 2. The method of to claim 1 wherein the determining the axialeye length comprises transforming a measured axial eye length to a humanpopulation average scale by addition of a transformation constant. 3.The method of claim 1, wherein the selected implantable IOL has at leastone aspheric curvature.
 4. The method of claim 1, wherein the selectedimplantable IOL has spherical curvatures.
 5. The method of claim 1,wherein the determining the aspheric representation of the corneacurvature comprises corneal topography and/or tomography.
 6. The methodof claim 5, wherein the aspheric representation of the cornea includes ak value for at least one corneal surface in combination with additionalmodifying terms.
 7. The method of claim 5, wherein the asphericrepresentation of the cornea includes a k value for both anterior andposterior corneal surfaces.
 8. The method of claim 1, wherein thecomputing with the ray tracing routine includes utilizing a focusing rayentering the pupil at 1/√{square root over (2)} an entrance pupilheight.
 9. The method of claim 1, wherein the computing with the raytracing routine includes tracing a marginal ray and a paraxial ray todetermine the midpoint between a foci of the marginal ray and a foci ofthe paraxial ray, as best focus of the eye model.
 10. The method ofclaim 1, wherein the computing with the ray tracing routine includestracing a marginal ray and a paraxial ray to determine the distancebetween a foci of the marginal ray and a foci of the paraxial ray as ametric for image quality.
 11. The method of claim 3, wherein theselected implantable IOL is described as having at least one surfacedescribed as modified conicoid according to the following formula:$x = {\frac{\left( \frac{1}{R} \right)y^{2}}{1 + \sqrt{1 - {{k\left( \frac{1}{R} \right)}^{2}y^{2}}}} + {a_{4}y^{4}} + {a_{6}y^{6}} + \ldots}$wherein R is the radius of curvature at the apex, k is the conicconstant, y is the radial distance from the optical axis and x is thesag in the direction of light propagation.
 12. The method of claim 4,wherein the eye of the subject has an oblate anterior corneal surfacewith a k value >1, or wherein the eye of the subject has a hyperboloidcorneal surface with a k value <0.
 13. The method of claim 1, furthercomprising measuring an anterior corneal apex radius, and wherein thedetermining the location of the lens haptic plane (LHP) comprisesutilizing the corneal apex radius.
 14. The method of claim 1 furthercomprising measuring both anterior and posterior corneal apex radii, andwherein the determining the location of the lens haptic plane (LHP)comprises utilizing the anterior and posterior corneal apex radii. 15.The method of claim 1, wherein, the location of the lens haptic plane isdetermined with a prediction algorithm that comprises input values ofmeasured axial eye length and at least one of the measured cornealradius and a corneal power (K).
 16. The method of claim 15, wherein theprediction algorithm is of the typeLHP=a+b×AL+c×ACD+d×LT+e×CR+f×AL ² +g×ACD ² +h×LT ² +i×CR ²+j×AL×ACD+k×AL×LT+l×AL×CR +m×ACD×LT+n×ACD×CR+o×LT×CR wherein AL is theaxial eye length, CR the corneal radius, or alternatively corneal power(K), ACD the anterior chamber depth, and LT the crystalline lensthickness.
 17. The method of claim 15, wherein said prediction algorithmfor the determining the location of the lens haptic plane in millimetersisLHP=2.486+0.2174×(AL+ΔAL)−0.4213×CR wherein AL is the measured axial eyelength, ΔAL is a transformation constant, which is specific for theequipment used to measure AL, and CR is the measured corneal radius. 18.The method of claim 1, wherein the location of the lens haptic plane isdirectly determined.
 19. The method of claim 18, wherein the location ofthe lens haptic plane is determined by ultrasound biomicroscopy.
 20. Themethod of claim 18, wherein the location of the lens haptic plane isdetermined by optical coherence tomography.
 21. The method of claim 18,wherein the location of the lens haptic plane is determined byScheimpflug photography.
 22. The method of claim 1, wherein the eye ofthe subject has undergone refractive corneal surgery thereby obtainingan oblate corneal surface.
 23. The method of claim 1, wherein the eye ofthe subject has undergone refractive corneal surgery thereby obtaining ahyperbolic corneal surface.
 24. The method of claim 1 wherein theselecting the implantable IOL comprises designing the implantable IOL toresult in the at least one of the desired postoperative refraction andthe desired postoperative spherical aberration.
 25. The method of claim1, wherein the desired light level comprises mesopic light conditions.26. An eye model suitable for selecting at least one combination ofpower and asphericity of an intraocular lens to be implanted in an eyeof a subject, comprising: an axial eye length based on a measured axialeye length transformed to a human population average scale by additionof a transformation constant; a pupil size at a desired light level; anaspheric representation of at least one corneal curvature; a lens hapticplane location for fixation of the intraocular lens followingimplantation; and a ray tracing routine configured to calculate anexpected at least one of a postoperative refraction and postoperativespherical aberration based at least in part on the axial eye length, thepupil size, the aspheric representation of the at least one cornealcurvature, and the lens haptic plane location; and wherein the eye modelis stored on a tangible computer readable memory.
 27. An eye modelaccording to claim 26, wherein the aspheric representation of the atleast one corneal curvature is derived from corneal topography and/ortomography.
 28. An eye model according to claim 27, wherein the asphericrepresentation of the at least one cornea curvature includes a k valuefor at least one corneal surface in combination with additionalmodifying terms.
 29. An eye model according to claim 27, wherein theaspheric representation of the at least one cornea curvature includes ak value for both anterior and posterior corneal surfaces.
 30. An eyemodel according to claim 28, wherein the aspheric representation of theat least one cornea curvature includes a k value >1 referring to acorneal oblate anterior corneal surface.
 31. An eye model according toclaim 26, wherein, the lens haptic plane location is obtained with aprediction algorithm that includes input values of measured axial eyelength and at least one of a measured corneal radius and a corneal power(K).
 32. An eye model according to claim 31, wherein the predictionalgorithm is of the typeLHP=a+b×AL+c×ACD+d×LT+e×CR +f×AL ² +g×ACD ² +h×LT ² +i×CR ²+j×AL×ACD+k×AL×LT+l×AL×CR +m×ACD×LT+n×ACD×CR+o×LT×CR wherein AL is theaxial eye length, CR the corneal radius, or alternatively corneal power(K), ACD the anterior chamber depth, and LT the crystalline lensthickness.
 33. An eye model according to claim 31, wherein saidprediction algorithm for the obtaining the lens haptic plane location inmillimeters isLHP=2.486+0.2174×(AL+ΔAL)−0.4213×CR wherein AL is the measured axial eyelength, ΔAL is a transformation constant, which is specific for theequipment used to measure AL, and CR is the measured corneal radius. 34.An eye model according to claim 26, wherein the lens haptic planelocation is directly determined.
 35. An eye model according to claim 34,wherein the lens haptic plane location is determined by means ofultrasound biomicroscopy.
 36. An eye model according to claim 34,wherein the lens haptic plane location is determined by means of opticalcoherence tomography.
 37. An eye model according to claim 34, whereinthe lens haptic plane location is determined by means of Scheimpflugphotography.
 38. A method of selecting an IOL to be implanted in the eyeof a subject comprising: a) determining an axial eye length, a pupilsize at a desired light level; b) determining an aspheric representationat least one corneal surface; c) selecting a first IOL and determining alocation of a plane of fixation of the first IOL following implantation;d) establishing an eye model; e) based on the eye model, the firstselected IOL, the axial eye length, the pupil size, the asphericrepresentation of the corneal curvature, and the plane of fixation,calculating an amount of postoperative spherical aberration using a raytracing routine; f) based on e), selecting an implantation IOL toprovide a selected amount of postoperative spherical aberration.
 39. Themethod of claim 38, wherein the selecting the implantation IOL furthercomprises: selecting a second IOL to replace the first IOL and repeatinge) and f) until the calculated amount of postoperative sphericalaberration is sufficiently close to the selected amount.
 40. A method ofselecting an IOL to be implanted in the eye of a subject, comprising:determining one or more ocular dimensions based on one or moremeasurements of at least one eye; selecting a desired postoperativerefractive outcome; selecting first IOL having at least one of a power,an aspheric profile, and a lens plane; establishing an eye model basedon the one or more characteristics of the at least one eye; determininga location of the lens plane; performing a calculation to determine apredicted postoperative refractive outcome based on the eye model, a raytracing algorithm, the location of the lens plane, and the selectedfirst IOL; comparing the predicted postoperative refractive outcome tothe desired refractive outcome; based on the comparison, repeating thecalculation with at least a second selected IOL having at least one of adifferent power, a different aspheric profile, and a different lensplane; and selecting an implantable IOL configured for implantation intothe eye of a subject based at least in part on the repeated calculation.41. The method of claim 40, wherein the desired postoperative refractiveoutcome comprises providing distant vision.
 42. The method of claim 40,wherein the desired postoperative refractive outcome comprises reducingan optical aberration of the eye.
 43. The method of claim 40, whereinthe lens plane is a lens haptic plane.
 44. The method of claim 40,wherein the selected implantable has an aspheric surface with apredetermined aspheric surface profile.
 45. The method of claim 40,wherein the one or more characteristics of the at least one eyecomprises an ocular pupil size.
 46. A computer system for selecting anIOL for placement into an eye of a subject, comprising: a processor; anda computer readable memory coupled to the processor, the memory havingstored therein: an array of ordered values, including: one or moreocular dimensions; a desired refractive outcome; at least one of apower, an aspheric profile, and a lens plane of one or more IOLs;parameters of an eye model based on one or more characteristics of atleast one eye; sequences of instructions which, when executed by theprocessor, cause the processor to select an implantable IOL configuredfor implantation into the eye of the subject, the sequences ofinstructions configured to: determine a location of the lens plane;perform a calculation to determine a predicted postoperative refractiveoutcome based on the eye model, the location of the lens plane, and aray tracing algorithm; compare the predicted postoperative refractiveoutcome to the desired refractive outcome; based on the comparison,repeat the calculation with an IOL having at least one of a differentpower, a different aspheric profile, and a different lens plane.